Bright Horizons Co. expects an EBIT of $12,500 every year in perpetuity. The firm currently has no debt, and its cost of equity is 12 percent. The company can borrow at an interest rate of 7 percent, and the corporate tax rate is 30 percent. What will the value of the firm be if it changes to a capital structure with 50 percent debt?

Question

BlackTom AI · Accepted Answer

Question restatement and options:
- The Bright Horizons Co. expects an EBIT of $12,500 every year in perpetuity.
- The firm currently has no debt, and its cost of equity is 12%.
- The company can borrow at an interest rate of 7%, and the corporate tax rate is 30%.
- What will the value of the firm be if it changes to a capital structure with 50% debt?
- Answer options: $83,854; $81,667; $76,885; $93,453

Step-by-step analysis of the underlying concepts and calculations:
- First, determine the value of the unlevered firm (no debt). When there is no debt, the firm’s cash flows are the EBIT after tax, i.e., EBIT*(1 - T). Here, EBIT = 12,500 and tax rate T = 30%, so after-tax operating cash flow is 12,500*(1 - 0.30) = 8,750 per year. For a perpetuity, the value of the unlevered firm, V_U, is these perpetual cash flows divided by the cost of equity (which equals the unlevered cost of capital when there is no debt): V_U = 8,750 / 0.12 = 72,916.67.
- Next, apply the classic tax shield reasoning for a levered firm with perpetual debt. The annual tax shield from debt is Tax_rate * Interest = T * (r_d * D). In the perpetuity model, the present value of the tax shields can be treated as an additional constant amount: PV(Tax shields) = T * D.
- Given the capital structure has 50% debt, D = 0.5 * V_L (the levered firm’s value). Therefore, V_L = V_U + PV(Tax shields) = V_U + T * D = V_U + 0.30 * (0.5 * V_L) = V_U + 0.15 * V_L.
- Solve for V_L: V_L - 0.15 * V_L = V_U ⇒ 0.85 * V_L = V_U ⇒ V_L = V_U / 0.85.
- Plugging in V_U = 72,916.67 gives V_L = 72,916.67 / 0.85 ≈ 85,781.96.
- Therefore, the calculated levered firm value under these assumptions is about $85,782 (rounded). Note that this relies on the standard, simplified perpetual debt tax shield model with no bankruptcy costs and constant debt, and uses the after-tax operating cash flow for the unlevered valuation.

Option-by-option evaluation:
- Option $83,854:
  - This value is somewhat close to the calculated $85,782 but somewhat lower. The discrepancy could arise from using a slightly different convention for the tax shield PV (for example, using PV(Tax shields) = 0.3 * D directly without the 0.5 scaling, or rounding in intermediate steps). In the strict derivation above, the result is about $85.8k, so $83,854 is not the exact result but is not wildly implausible if one uses alternative tax shield assumptions.
- Option $81,667:
  - This is noticeably lower than the computed $85.8k. It would require a larger deduction from the tax shield or a smaller unlevered value, which would come from either a lower after-tax cash flow realization or a different treatment of the tax shield, neither of which aligns with the standard perpetual debt tax shield model used here.
- Option $76,885:
  - This is considerably lower than the derived value. It would imply a substantially smaller V_U or a smaller PV of tax shields than the model yields, incompatible with the given perpetual EBIT and tax rate under the standard M&M framework used for perpetual debt with a fixed debt ratio.
- Option $93,453:
  - This is higher than the calculated $85.8k. Achieving this would require a larger PV of the tax shield or a larger unlevered firm value, which would necessitate either a higher EBIT, a lower tax rate, or a more favorable leverage effect than assumed. Under the specified inputs, this option overstates the levered value relative to the standard calculation.

Summary note:
- Using the conventional perpetual debt tax shield approach with D = 0.5 V_L yields V_L ≈ 85,782. The provided answer choices include values near this figure but do not match exactly; among them, $83,854 is the closest to the derived result, while the others diverge more significantly. Remember that small differences can stem from rounding conventions or alternative tax shield modeling assumptions.

类似问题

Which of the following statements best reflects the key insight of the M&M Proposition (without taxes)?

In a world with perfect capital markets, a firm that issues a large amount debt to finance a share repurchase will ultimately boost its EPS and reduce its post-transaction market capitalization, but will not affect its stock price.

In a world with corporate taxes (only capital markets imperfection), a levered firm will issue equity to repay some of its debt. Indicate which of the following statements is correct:

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